Publications by Colleges and Departments (MSU - Bozeman)
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Item Comment on “dielectric study of the ferroelectric transition of KH2PO4”(1976-08) Western, Arthur B.; Schmidt, V. HugoWe reanalyze a.c. dielectric data taken by Eberhard and Horn for KH2PO4 near Tc, and obtain a much lower value of the critical bias field, near 300 V/cm in accord with results found by other workers.Item One-dimensional model for cooperative hydrogen motion in ferroelectric crystals(1974-01) Schmidt, V. HugoThe static and dynamic behavior is examined for “Takagi groups” in double-minimum potential wells containing protons (or deuterons) coupled by harmonic forces. Predictions of this model are compared with observed isotope effects on domain wall mobility and dielectric relaxation in KH2PO4. The model predicts effects previously attributed to tunneling.Item Spin-Lattice Relaxation of Al^{27} in Thulium Aluminum Garnet(1973-05) Trontelj, Z.; Schmidt, V. HugoThe Al27 spin-lattice relaxation time T1 has been measured between 127 and 425 °K at 8 and 14 MHz for the aluminum a and d sites in thulium aluminum garnet. Both sites exhibit T1 dips at 275 °K which are attributed to Al27-Tm169 cross relaxation. Below 190 °K the a-site T1 magnitudes and approximately ω−2 frequency dependence are explained by magnetic field fluctuations caused by the Tm3+ ion making transitions between its two lowest crystal-field levels with a correlation time near 4 × 10−12 sec.Item Pressure-induced tricritical point in the ferroelectric phase transition of KH_{2}PO_{4}(1978-06) Western, Arthur B.; Baker, A. G.; Bacon, Charles R.; Schmidt, V. HugoMeasurement of the net polarization charge of two KH2PO4 crystals as a function of temperature, applied electric field, and hydrostatic pressure indicates the existence of a tricritical point in the (2.3±0.3)-kbar pressure range. This result is based upon static measurements of the polarization response to applied dc field in a 0.5-K neighborhood of the ferroelectric transition at pressures of 0, 1, 2, 2.4, and 3 kbar. Unlike He3- He4 mixtures and some metamagnets, for KH2PO4 the field which gives rise to the "wing" structure of the tricritical point is experimentally available. For each of the five pressures the paraelectric region is well described by the Landau equation of state, E=A0(T−T0)P+BP3+CP5, to within 0.05 K of the transition temperature. The exponent δ derived from our data at 3 kbar is in the crossover region between the critical value of 3 and the tricritical value of 5 predicted by Landau theory. At 2.4 kbar our derived value of δ is consistent with the tricritical value of 5. Analysis of the data along lines of constant polarization, which are here called "isopols," indicates that the transition is first order at 0 and 1 kbar with the critical field decreasing from 183±60 V/cm at 0 kbar to 43±13 V/cm at 1 kbar. At 3 kbar the B coefficient is positive which indicates a second-order transition. This observation of a change in the order of the transition is supported by a change in the behavior of the isothermal dielectric susceptibility which has a maximum for E>0 at 0.5 kbar and at E=0 at 3 kbar.Item Dipolar Relaxation of 7Li by Hindered Rotators NDxH3−x in Lithimn Hydrazinium Sulfate.(1972-04) Parker, Robert S.; Schmidt, V. HugoWhen a hindered rotation does not change the spatial charge distribution but merely permutes the locations of nuclear magnetic moments, the resulting spin-lattice relaxation of a nearby fixed nucleus is likely to be dipolar even if this nucleus has a quadrupole moment. The dipolar relaxation rate is props rtional to the average of γ2I(I + 1) for the rotating nuclei and accordingly varies linearly with percentage of deuteration. For 7Li in LiN2H5SO4 at 14 MHz the peak is 1.8 sec− at 185°K, while in 81% deuterated LiN2D5SO4 it is 4.2 times smaller, as predicted. The ND2 group deuterons also have a peak at this temperature, and all three curves show activation energy of about 0.19 eV, as found previously for protons and deuterons within rotating NH3 and ND3 groups.Item Nuclear-Magnetic-Rosonance Study of Thulium Aluminum Garnet(1970-03) Jones, E. D.; Schmidt, V. HugoThe Tm169 and the Al27 nuclear magnetic resonance have been studied in cubic thulium aluminum garnet. The Tm169 results at 1.5°K give magnetic-susceptibility tensor components of χ1=0.014, χ2=0.551, and and χ3=0.030 emu/g ion, which show much more anisotropy than found previously for thulium gallium garnet. The measured Al27 paramagnetic shifts at 1.5°K agree quite well with values calculated from Tm3+-ion dipole sums. The Al27 paramagnetic shifts from 1.5 to 300°K are used to calculate the approximate temperature dependence of the Tm2+-ion susceptibility components. The room-temperature Al27 quadrupolar coupling constants ∣∣e2qQh∣∣ for the axially symmetric a and d sites are 0.892±0.005 and 6.155±0.005 MHz, respectively. The unshielded electric field gradients are calculated and compared with corresponding values for other aluminum garnets and for Fe57 sites in several iron garnets. These field gradients agree quite well with values calculated using a point-charge model.Item Deuteron NMR Study of Lithium Hydrazinium Sulfate(1969-09) Howell, Francis L.; Schmidt, V. HugoThe magnetic resonance spectrum of the deuterons in single crystals of LiN2D5SO4 has been studied between 78 and 458°K. The electric quadrupole coupling constants, the asymmetry parameters, and the orientations of the electric field gradient (efg) tensors relative to the crystal axes were obtained at 78°K, 193°K, 25°C, 65°C, and 95°C. The orientations of the efg tensors are considered in relation to nearby atomic sites. At 78°K the spectrum contains distinct lines due to the five deuterons of the N2D5 + ion. Between 110 and 150°K the lines due to the three deuterons of the ND3 group broaden and merge to a single pair which is still visible at 185°C. A small change with temperature in the coupling constant associated with this pair of lines is discussed. The lines due to the two deuterons of the ND2 group broaden and merge to a single pair between 0 and 50°C. These line mergers result from hindered rotation of the ND2 and ND3 groups. Estimates of the activation energies for these motions are made. These changes in the spectrum are related to the results of earlier NMR studies and to previous electrical conductivity and dielectric constant measurements.Item Electrical Conductivity of (NH4)2SO4 Single Crystals(American Institute of Physics, 1963-06) Schmidt, V. Hugo